Determine the area under the standard normal curve that lies to the left of (a) $$ Z=0.99 $$, (b) $$ Z=-1.31 $$, (c) $$ Z=-1.37 $$, and (d) $$ Z=0.24 $$. (a) The area to the left of $$ Z=0.99 $$ is $$ \square $$. (Round to four decimal places as needed.) (b) The area to the left of $$ Z=-1.31 $$ is $$ \square $$. (Round to four decimal places as needed.) (c) The area to the left of $$ Z=-1.37 $$ is $$ \square $$. (Round to four decimal places as needed.) (d) The area to the left of $$ Z=0.24 $$ is $$ \square $$. (Round to four decimal places as needed.)

Question

UpStudy AI · Accepted Answer

First, we recall that the area to the left of a given $$ Z $$ value, denoted $$ P(Z < z) $$, is obtained from the standard normal cumulative distribution function.

**(a) For $$ Z=0.99 $$:**

Using a standard normal table or calculator, we find
$$
P(Z<0.99) \approx 0.8389.
$$

**(b) For $$ Z=-1.31 $$:**

Typically, tables give values for positive $$ Z $$. Using the symmetry of the standard normal distribution:
$$
P(Z<-1.31) = 1 - P(Z<1.31).
$$
For $$ Z = 1.31 $$,
$$
P(Z<1.31) \approx 0.9049.
$$
Thus,
$$
P(Z<-1.31) \approx 1 - 0.9049 = 0.0951.
$$

**(c) For $$ Z=-1.37 $$:**

Similarly, for $$ Z = -1.37 $$:
$$
P(Z<-1.37) = 1 - P(Z<1.37).
$$
For $$ Z = 1.37 $$,
$$
P(Z<1.37) \approx 0.9147.
$$
Thus,
$$
P(Z<-1.37) \approx 1 - 0.9147 = 0.0853.
$$

**(d) For $$ Z=0.24 $$:**

From the standard normal table,
$$
P(Z<0.24) \approx 0.5948.
$$

So the answers, rounded to four decimal places, are:

(a) The area to the left of $$ Z=0.99 $$ is $$ 0.8389 $$.

(b) The area to the left of $$ Z=-1.31 $$ is $$ 0.0951 $$.

(c) The area to the left of $$ Z=-1.37 $$ is $$ 0.0853 $$.

(d) The area to the left of $$ Z=0.24 $$ is $$ 0.5948 $$.
(a) The area to the left of $$ Z=0.99 $$ is $$ 0.8389 $$. (b) The area to the left of $$ Z=-1.31 $$ is $$ 0.0951 $$. (c) The area to the left of $$ Z=-1.37 $$ is $$ 0.0853 $$. (d) The area to the left of $$ Z=0.24 $$ is $$ 0.5948 $$.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Statistics Questions